
theorem
  1861 is prime
proof
  now
    1861 = 2*930 + 1; hence not 2 divides 1861 by NAT_4:9;
    1861 = 3*620 + 1; hence not 3 divides 1861 by NAT_4:9;
    1861 = 5*372 + 1; hence not 5 divides 1861 by NAT_4:9;
    1861 = 7*265 + 6; hence not 7 divides 1861 by NAT_4:9;
    1861 = 11*169 + 2; hence not 11 divides 1861 by NAT_4:9;
    1861 = 13*143 + 2; hence not 13 divides 1861 by NAT_4:9;
    1861 = 17*109 + 8; hence not 17 divides 1861 by NAT_4:9;
    1861 = 19*97 + 18; hence not 19 divides 1861 by NAT_4:9;
    1861 = 23*80 + 21; hence not 23 divides 1861 by NAT_4:9;
    1861 = 29*64 + 5; hence not 29 divides 1861 by NAT_4:9;
    1861 = 31*60 + 1; hence not 31 divides 1861 by NAT_4:9;
    1861 = 37*50 + 11; hence not 37 divides 1861 by NAT_4:9;
    1861 = 41*45 + 16; hence not 41 divides 1861 by NAT_4:9;
    1861 = 43*43 + 12; hence not 43 divides 1861 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1861 & n is prime
  holds not n divides 1861 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
